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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    package org.apache.commons.math3.analysis.integration;<a name="line.17"></a>
<FONT color="green">018</FONT>    <a name="line.18"></a>
<FONT color="green">019</FONT>    import org.apache.commons.math3.exception.MaxCountExceededException;<a name="line.19"></a>
<FONT color="green">020</FONT>    import org.apache.commons.math3.exception.NotStrictlyPositiveException;<a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math3.exception.NumberIsTooLargeException;<a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math3.exception.NumberIsTooSmallException;<a name="line.22"></a>
<FONT color="green">023</FONT>    import org.apache.commons.math3.exception.TooManyEvaluationsException;<a name="line.23"></a>
<FONT color="green">024</FONT>    import org.apache.commons.math3.util.FastMath;<a name="line.24"></a>
<FONT color="green">025</FONT>    <a name="line.25"></a>
<FONT color="green">026</FONT>    /**<a name="line.26"></a>
<FONT color="green">027</FONT>     * Implements the &lt;a href="http://mathworld.wolfram.com/RombergIntegration.html"&gt;<a name="line.27"></a>
<FONT color="green">028</FONT>     * Romberg Algorithm&lt;/a&gt; for integration of real univariate functions. For<a name="line.28"></a>
<FONT color="green">029</FONT>     * reference, see &lt;b&gt;Introduction to Numerical Analysis&lt;/b&gt;, ISBN 038795452X,<a name="line.29"></a>
<FONT color="green">030</FONT>     * chapter 3.<a name="line.30"></a>
<FONT color="green">031</FONT>     * &lt;p&gt;<a name="line.31"></a>
<FONT color="green">032</FONT>     * Romberg integration employs k successive refinements of the trapezoid<a name="line.32"></a>
<FONT color="green">033</FONT>     * rule to remove error terms less than order O(N^(-2k)). Simpson's rule<a name="line.33"></a>
<FONT color="green">034</FONT>     * is a special case of k = 2.&lt;/p&gt;<a name="line.34"></a>
<FONT color="green">035</FONT>     *<a name="line.35"></a>
<FONT color="green">036</FONT>     * @version $Id: RombergIntegrator.java 1364387 2012-07-22 18:14:11Z tn $<a name="line.36"></a>
<FONT color="green">037</FONT>     * @since 1.2<a name="line.37"></a>
<FONT color="green">038</FONT>     */<a name="line.38"></a>
<FONT color="green">039</FONT>    public class RombergIntegrator extends BaseAbstractUnivariateIntegrator {<a name="line.39"></a>
<FONT color="green">040</FONT>    <a name="line.40"></a>
<FONT color="green">041</FONT>        /** Maximal number of iterations for Romberg. */<a name="line.41"></a>
<FONT color="green">042</FONT>        public static final int ROMBERG_MAX_ITERATIONS_COUNT = 32;<a name="line.42"></a>
<FONT color="green">043</FONT>    <a name="line.43"></a>
<FONT color="green">044</FONT>        /**<a name="line.44"></a>
<FONT color="green">045</FONT>         * Build a Romberg integrator with given accuracies and iterations counts.<a name="line.45"></a>
<FONT color="green">046</FONT>         * @param relativeAccuracy relative accuracy of the result<a name="line.46"></a>
<FONT color="green">047</FONT>         * @param absoluteAccuracy absolute accuracy of the result<a name="line.47"></a>
<FONT color="green">048</FONT>         * @param minimalIterationCount minimum number of iterations<a name="line.48"></a>
<FONT color="green">049</FONT>         * @param maximalIterationCount maximum number of iterations<a name="line.49"></a>
<FONT color="green">050</FONT>         * (must be less than or equal to {@link #ROMBERG_MAX_ITERATIONS_COUNT})<a name="line.50"></a>
<FONT color="green">051</FONT>         * @exception NotStrictlyPositiveException if minimal number of iterations<a name="line.51"></a>
<FONT color="green">052</FONT>         * is not strictly positive<a name="line.52"></a>
<FONT color="green">053</FONT>         * @exception NumberIsTooSmallException if maximal number of iterations<a name="line.53"></a>
<FONT color="green">054</FONT>         * is lesser than or equal to the minimal number of iterations<a name="line.54"></a>
<FONT color="green">055</FONT>         * @exception NumberIsTooLargeException if maximal number of iterations<a name="line.55"></a>
<FONT color="green">056</FONT>         * is greater than {@link #ROMBERG_MAX_ITERATIONS_COUNT}<a name="line.56"></a>
<FONT color="green">057</FONT>         */<a name="line.57"></a>
<FONT color="green">058</FONT>        public RombergIntegrator(final double relativeAccuracy,<a name="line.58"></a>
<FONT color="green">059</FONT>                                 final double absoluteAccuracy,<a name="line.59"></a>
<FONT color="green">060</FONT>                                 final int minimalIterationCount,<a name="line.60"></a>
<FONT color="green">061</FONT>                                 final int maximalIterationCount)<a name="line.61"></a>
<FONT color="green">062</FONT>            throws NotStrictlyPositiveException, NumberIsTooSmallException, NumberIsTooLargeException {<a name="line.62"></a>
<FONT color="green">063</FONT>            super(relativeAccuracy, absoluteAccuracy, minimalIterationCount, maximalIterationCount);<a name="line.63"></a>
<FONT color="green">064</FONT>            if (maximalIterationCount &gt; ROMBERG_MAX_ITERATIONS_COUNT) {<a name="line.64"></a>
<FONT color="green">065</FONT>                throw new NumberIsTooLargeException(maximalIterationCount,<a name="line.65"></a>
<FONT color="green">066</FONT>                                                    ROMBERG_MAX_ITERATIONS_COUNT, false);<a name="line.66"></a>
<FONT color="green">067</FONT>            }<a name="line.67"></a>
<FONT color="green">068</FONT>        }<a name="line.68"></a>
<FONT color="green">069</FONT>    <a name="line.69"></a>
<FONT color="green">070</FONT>        /**<a name="line.70"></a>
<FONT color="green">071</FONT>         * Build a Romberg integrator with given iteration counts.<a name="line.71"></a>
<FONT color="green">072</FONT>         * @param minimalIterationCount minimum number of iterations<a name="line.72"></a>
<FONT color="green">073</FONT>         * @param maximalIterationCount maximum number of iterations<a name="line.73"></a>
<FONT color="green">074</FONT>         * (must be less than or equal to {@link #ROMBERG_MAX_ITERATIONS_COUNT})<a name="line.74"></a>
<FONT color="green">075</FONT>         * @exception NotStrictlyPositiveException if minimal number of iterations<a name="line.75"></a>
<FONT color="green">076</FONT>         * is not strictly positive<a name="line.76"></a>
<FONT color="green">077</FONT>         * @exception NumberIsTooSmallException if maximal number of iterations<a name="line.77"></a>
<FONT color="green">078</FONT>         * is lesser than or equal to the minimal number of iterations<a name="line.78"></a>
<FONT color="green">079</FONT>         * @exception NumberIsTooLargeException if maximal number of iterations<a name="line.79"></a>
<FONT color="green">080</FONT>         * is greater than {@link #ROMBERG_MAX_ITERATIONS_COUNT}<a name="line.80"></a>
<FONT color="green">081</FONT>         */<a name="line.81"></a>
<FONT color="green">082</FONT>        public RombergIntegrator(final int minimalIterationCount,<a name="line.82"></a>
<FONT color="green">083</FONT>                                 final int maximalIterationCount)<a name="line.83"></a>
<FONT color="green">084</FONT>            throws NotStrictlyPositiveException, NumberIsTooSmallException, NumberIsTooLargeException {<a name="line.84"></a>
<FONT color="green">085</FONT>            super(minimalIterationCount, maximalIterationCount);<a name="line.85"></a>
<FONT color="green">086</FONT>            if (maximalIterationCount &gt; ROMBERG_MAX_ITERATIONS_COUNT) {<a name="line.86"></a>
<FONT color="green">087</FONT>                throw new NumberIsTooLargeException(maximalIterationCount,<a name="line.87"></a>
<FONT color="green">088</FONT>                                                    ROMBERG_MAX_ITERATIONS_COUNT, false);<a name="line.88"></a>
<FONT color="green">089</FONT>            }<a name="line.89"></a>
<FONT color="green">090</FONT>        }<a name="line.90"></a>
<FONT color="green">091</FONT>    <a name="line.91"></a>
<FONT color="green">092</FONT>        /**<a name="line.92"></a>
<FONT color="green">093</FONT>         * Construct a Romberg integrator with default settings<a name="line.93"></a>
<FONT color="green">094</FONT>         * (max iteration count set to {@link #ROMBERG_MAX_ITERATIONS_COUNT})<a name="line.94"></a>
<FONT color="green">095</FONT>         */<a name="line.95"></a>
<FONT color="green">096</FONT>        public RombergIntegrator() {<a name="line.96"></a>
<FONT color="green">097</FONT>            super(DEFAULT_MIN_ITERATIONS_COUNT, ROMBERG_MAX_ITERATIONS_COUNT);<a name="line.97"></a>
<FONT color="green">098</FONT>        }<a name="line.98"></a>
<FONT color="green">099</FONT>    <a name="line.99"></a>
<FONT color="green">100</FONT>        /** {@inheritDoc} */<a name="line.100"></a>
<FONT color="green">101</FONT>        @Override<a name="line.101"></a>
<FONT color="green">102</FONT>        protected double doIntegrate()<a name="line.102"></a>
<FONT color="green">103</FONT>            throws TooManyEvaluationsException, MaxCountExceededException {<a name="line.103"></a>
<FONT color="green">104</FONT>    <a name="line.104"></a>
<FONT color="green">105</FONT>            final int m = iterations.getMaximalCount() + 1;<a name="line.105"></a>
<FONT color="green">106</FONT>            double previousRow[] = new double[m];<a name="line.106"></a>
<FONT color="green">107</FONT>            double currentRow[]  = new double[m];<a name="line.107"></a>
<FONT color="green">108</FONT>    <a name="line.108"></a>
<FONT color="green">109</FONT>            TrapezoidIntegrator qtrap = new TrapezoidIntegrator();<a name="line.109"></a>
<FONT color="green">110</FONT>            currentRow[0] = qtrap.stage(this, 0);<a name="line.110"></a>
<FONT color="green">111</FONT>            iterations.incrementCount();<a name="line.111"></a>
<FONT color="green">112</FONT>            double olds = currentRow[0];<a name="line.112"></a>
<FONT color="green">113</FONT>            while (true) {<a name="line.113"></a>
<FONT color="green">114</FONT>    <a name="line.114"></a>
<FONT color="green">115</FONT>                final int i = iterations.getCount();<a name="line.115"></a>
<FONT color="green">116</FONT>    <a name="line.116"></a>
<FONT color="green">117</FONT>                // switch rows<a name="line.117"></a>
<FONT color="green">118</FONT>                final double[] tmpRow = previousRow;<a name="line.118"></a>
<FONT color="green">119</FONT>                previousRow = currentRow;<a name="line.119"></a>
<FONT color="green">120</FONT>                currentRow = tmpRow;<a name="line.120"></a>
<FONT color="green">121</FONT>    <a name="line.121"></a>
<FONT color="green">122</FONT>                currentRow[0] = qtrap.stage(this, i);<a name="line.122"></a>
<FONT color="green">123</FONT>                iterations.incrementCount();<a name="line.123"></a>
<FONT color="green">124</FONT>                for (int j = 1; j &lt;= i; j++) {<a name="line.124"></a>
<FONT color="green">125</FONT>                    // Richardson extrapolation coefficient<a name="line.125"></a>
<FONT color="green">126</FONT>                    final double r = (1L &lt;&lt; (2 * j)) - 1;<a name="line.126"></a>
<FONT color="green">127</FONT>                    final double tIJm1 = currentRow[j - 1];<a name="line.127"></a>
<FONT color="green">128</FONT>                    currentRow[j] = tIJm1 + (tIJm1 - previousRow[j - 1]) / r;<a name="line.128"></a>
<FONT color="green">129</FONT>                }<a name="line.129"></a>
<FONT color="green">130</FONT>                final double s = currentRow[i];<a name="line.130"></a>
<FONT color="green">131</FONT>                if (i &gt;= getMinimalIterationCount()) {<a name="line.131"></a>
<FONT color="green">132</FONT>                    final double delta  = FastMath.abs(s - olds);<a name="line.132"></a>
<FONT color="green">133</FONT>                    final double rLimit = getRelativeAccuracy() * (FastMath.abs(olds) + FastMath.abs(s)) * 0.5;<a name="line.133"></a>
<FONT color="green">134</FONT>                    if ((delta &lt;= rLimit) || (delta &lt;= getAbsoluteAccuracy())) {<a name="line.134"></a>
<FONT color="green">135</FONT>                        return s;<a name="line.135"></a>
<FONT color="green">136</FONT>                    }<a name="line.136"></a>
<FONT color="green">137</FONT>                }<a name="line.137"></a>
<FONT color="green">138</FONT>                olds = s;<a name="line.138"></a>
<FONT color="green">139</FONT>            }<a name="line.139"></a>
<FONT color="green">140</FONT>    <a name="line.140"></a>
<FONT color="green">141</FONT>        }<a name="line.141"></a>
<FONT color="green">142</FONT>    <a name="line.142"></a>
<FONT color="green">143</FONT>    }<a name="line.143"></a>




























































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